Project Euler 5 in Python - How can I optimize my solution?

Question

I\'ve recently been working on Project Euler problems in Python. I am fairly new to Python, and still somewhat new as a programmer.

In any case, I\'ve ran into a sp

Answer 1

I wrote a solution to euler5 that:

• Is orders of magnitude faster than most of the solutions here when n=20 (though not all respondents report their time) because it uses no imports (other than to measure time for this answer) and only basic data structures in python.

• Scales much better than most other solutions. It will give the answer for n=20 in 6e-05 seconds, or for n=100 in 1 millisec, faster than most of the responses for n=20 listed here.

  import time
  a=time.clock() # set timer
  
  j=1
  factorlist=[]
  mydict={}
  # change second number to desired number +1 if the question were changed.
  for i in range(2,21,1):
      numberfactors=[]
      num=i
      j=2
  # build a list of the prime factors
      for j in range(j,num+1,1):
          counter=0
          if i%j==0:
              while i%j==0:
                  counter+=1
                  numberfactors.append(j)
                  i=i/j
  # add a list of factors to a dictionary, with each prime factor as a key
                  if j not in mydict:
                      mydict[j] = counter
  # now, if a factor is already present n times, including n times the factor
  # won't increase the LCM. So replace the dictionary key with the max number of
  # unique factors if and only if the number of times it appears is greater than
  # the number of times it has already appeared.
  # for example, the prime factors of 8 are 2,2, and 2. This would be replaced 
  # in the dictionary once 16 were found (prime factors 2,2,2, and 2).
              elif mydict[j] < counter:
                  mydict[j]=counter
  
  total=1
  for key, value in mydict.iteritems():
      key=int(key)
      value=int(value)
      total=total*(key**value)
  
  b=time.clock()
  elapsed_time=b-a
  print total, "calculated in", elapsed_time, "seconds"
  

  returns:

  232792560 calculated in 6e-05 seconds
  
  # does not rely on heuristics unknown to all users, for instance the idea that 
  # we only need to include numbers above 10, etc.
  
  
  # For all numbers evenly divisible by 1 through 100:
  69720375229712477164533808935312303556800 calculated in 0.001335 seconds